"""simple docstring"""



import math

import torch
from torch import nn

from ..configuration_utils import ConfigMixin, register_to_config
from .attention_processor import Attention
from .embeddings import get_timestep_embedding
from .modeling_utils import ModelMixin






class  snake_case__      (       snake_case_,						snake_case_       ):


 @register_to_config
 def __init__( self    ,		lowerCamelCase = 128    ,		lowerCamelCase = 256    ,		lowerCamelCase = 2000.0    ,		lowerCamelCase = 768    ,		lowerCamelCase = 12    ,		lowerCamelCase = 12    ,		lowerCamelCase = 64    ,		lowerCamelCase = 2048    ,		lowerCamelCase = 0.1    ,		):
        super().__init__()

        __a       =    nn.Sequential(
            nn.Linear(lowerCamelCase    ,		d_model * 4    ,		bias=lowerCamelCase						)    ,		nn.SiLU()    ,		nn.Linear(d_model * 4    ,		d_model * 4    ,		bias=lowerCamelCase						)    ,		nn.SiLU()    ,		)

        __a       =    nn.Embedding(lowerCamelCase    ,		lowerCamelCase						)
        __a       =    False

        __a       =    nn.Linear(lowerCamelCase    ,		lowerCamelCase    ,		bias=lowerCamelCase						)

        __a       =    nn.Dropout(p=lowerCamelCase						)

        __a       =    nn.ModuleList()
        for lyr_num in range(lowerCamelCase						):
               # FiLM conditional T5 decoder
               __a       =    DecoderLayer(d_model=lowerCamelCase    ,		d_kv=lowerCamelCase    ,		num_heads=lowerCamelCase    ,		d_ff=lowerCamelCase    ,		dropout_rate=lowerCamelCase						)
               self.decoders.append(lowerCamelCase						)

        __a       =    TaLayerNorm(lowerCamelCase						)

        __a       =    nn.Dropout(p=lowerCamelCase						)
        __a       =    nn.Linear(lowerCamelCase    ,		lowerCamelCase    ,		bias=lowerCamelCase						)


 def 						a__   ( self    ,		lowerCamelCase    ,		lowerCamelCase						):
        __a       =    torch.mul(query_input.unsqueeze(-1						)    ,		key_input.unsqueeze(-2						)						)
        return mask.unsqueeze(-3						)






 def 						a__   ( self    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase						):
        __a ,   __a ,   __a       =    decoder_input_tokens.shape
        assert decoder_noise_time.shape == (batch,)

        # decoder_noise_time is in [0, 1), so rescale to expected timing range.
        __a       =    get_timestep_embedding(
            decoder_noise_time * self.config.max_decoder_noise_time    ,		embedding_dim=self.config.d_model    ,		max_period=self.config.max_decoder_noise_time    ,		).to(dtype=self.dtype						)

        __a       =    self.conditioning_emb(lowerCamelCase						).unsqueeze(1						)

        assert conditioning_emb.shape == (batch, 1, self.config.d_model * 4)

        __a       =    decoder_input_tokens.shape[1]

        # If we want to use relative positions for audio context, we can just offset
        # this sequence by the length of encodings_and_masks.
        __a       =    torch.broadcast_to(
            torch.arange(lowerCamelCase    ,		device=decoder_input_tokens.device						)    ,		(batch, seq_length)    ,		)

        __a       =    self.position_encoding(lowerCamelCase						)

        __a       =    self.continuous_inputs_projection(lowerCamelCase						)
        inputs += position_encodings
        __a       =    self.dropout(lowerCamelCase						)

        # decoder: No padding present.
        __a       =    torch.ones(
            decoder_input_tokens.shape[:2]    ,		device=decoder_input_tokens.device    ,		dtype=inputs.dtype						)

        # Translate encoding masks to encoder-decoder masks.
        __a       =    [(x, self.encoder_decoder_mask(lowerCamelCase    ,		lowerCamelCase						)) for x, y in encodings_and_masks]

        # cross attend style: concat encodings
        __a       =    torch.cat([x[0] for x in encodings_and_encdec_masks]    ,		dim=1						)
        __a       =    torch.cat([x[1] for x in encodings_and_encdec_masks]    ,		dim=-1						)

        for lyr in self.decoders:
               __a       =    lyr(
                   lowerCamelCase    ,		conditioning_emb=lowerCamelCase    ,		encoder_hidden_states=lowerCamelCase    ,		encoder_attention_mask=lowerCamelCase    ,		)[0]

        __a       =    self.decoder_norm(lowerCamelCase						)
        __a       =    self.post_dropout(lowerCamelCase						)

        __a       =    self.spec_out(lowerCamelCase						)
        return spec_out






class  snake_case__      (       nn.Module       ):


 def __init__( self    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase=1E-6						):
        super().__init__()
        __a       =    nn.ModuleList()

        # cond self attention: layer 0
        self.layer.append(
            TaLayerSelfAttentionCond(d_model=lowerCamelCase    ,		d_kv=lowerCamelCase    ,		num_heads=lowerCamelCase    ,		dropout_rate=lowerCamelCase						)						)

        # cross attention: layer 1
        self.layer.append(
            TaLayerCrossAttention(
                d_model=lowerCamelCase    ,		d_kv=lowerCamelCase    ,		num_heads=lowerCamelCase    ,		dropout_rate=lowerCamelCase    ,		layer_norm_epsilon=lowerCamelCase    ,		)						)

        # Film Cond MLP + dropout: last layer
        self.layer.append(
            TaLayerFFCond(d_model=lowerCamelCase    ,		d_ff=lowerCamelCase    ,		dropout_rate=lowerCamelCase    ,		layer_norm_epsilon=lowerCamelCase						)						)






 def 						a__   ( self    ,		lowerCamelCase    ,		lowerCamelCase=None    ,		lowerCamelCase=None    ,		lowerCamelCase=None    ,		lowerCamelCase=None    ,		lowerCamelCase=None    ,		):
        __a       =    self.layer[0](
            lowerCamelCase    ,		conditioning_emb=lowerCamelCase    ,		attention_mask=lowerCamelCase    ,		)

        if encoder_hidden_states is not None:
               __a       =    torch.where(encoder_attention_mask > 0    ,		0    ,		-1E10						).to(
                   encoder_hidden_states.dtype						)

               __a       =    self.layer[1](
                   lowerCamelCase    ,		key_value_states=lowerCamelCase    ,		attention_mask=lowerCamelCase    ,		)

        # Apply Film Conditional Feed Forward layer
        __a       =    self.layer[-1](lowerCamelCase    ,		lowerCamelCase						)

        return (hidden_states,)






class  snake_case__      (       nn.Module       ):


 def __init__( self    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase						):
        super().__init__()
        __a       =    TaLayerNorm(lowerCamelCase						)
        __a       =    TaFiLMLayer(in_features=d_model * 4    ,		out_features=lowerCamelCase						)
        __a       =    Attention(query_dim=lowerCamelCase    ,		heads=lowerCamelCase    ,		dim_head=lowerCamelCase    ,		out_bias=lowerCamelCase    ,		scale_qk=lowerCamelCase						)
        __a       =    nn.Dropout(lowerCamelCase						)






 def 						a__   ( self    ,		lowerCamelCase    ,		lowerCamelCase=None    ,		lowerCamelCase=None    ,		):
        # pre_self_attention_layer_norm
        __a       =    self.layer_norm(lowerCamelCase						)

        if conditioning_emb is not None:
               __a       =    self.FiLMLayer(lowerCamelCase    ,		lowerCamelCase						)

        # Self-attention block
        __a       =    self.attention(lowerCamelCase						)

        __a       =    hidden_states + self.dropout(lowerCamelCase						)

        return hidden_states






class  snake_case__      (       nn.Module       ):


 def __init__( self    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase						):
        super().__init__()
        __a       =    Attention(query_dim=lowerCamelCase    ,		heads=lowerCamelCase    ,		dim_head=lowerCamelCase    ,		out_bias=lowerCamelCase    ,		scale_qk=lowerCamelCase						)
        __a       =    TaLayerNorm(lowerCamelCase    ,		eps=lowerCamelCase						)
        __a       =    nn.Dropout(lowerCamelCase						)






 def 						a__   ( self    ,		lowerCamelCase    ,		lowerCamelCase=None    ,		lowerCamelCase=None    ,		):
        __a       =    self.layer_norm(lowerCamelCase						)
        __a       =    self.attention(
            lowerCamelCase    ,		encoder_hidden_states=lowerCamelCase    ,		attention_mask=attention_mask.squeeze(1						)    ,		)
        __a       =    hidden_states + self.dropout(lowerCamelCase						)
        return layer_output






class  snake_case__      (       nn.Module       ):


 def __init__( self    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase						):
        super().__init__()
        __a       =    TaDenseGatedActDense(d_model=lowerCamelCase    ,		d_ff=lowerCamelCase    ,		dropout_rate=lowerCamelCase						)
        __a       =    TaFiLMLayer(in_features=d_model * 4    ,		out_features=lowerCamelCase						)
        __a       =    TaLayerNorm(lowerCamelCase    ,		eps=lowerCamelCase						)
        __a       =    nn.Dropout(lowerCamelCase						)






 def 						a__   ( self    ,		lowerCamelCase    ,		lowerCamelCase=None						):
        __a       =    self.layer_norm(lowerCamelCase						)
        if conditioning_emb is not None:
               __a       =    self.film(lowerCamelCase    ,		lowerCamelCase						)

        __a       =    self.DenseReluDense(lowerCamelCase						)
        __a       =    hidden_states + self.dropout(lowerCamelCase						)
        return hidden_states






class  snake_case__      (       nn.Module       ):


 def __init__( self    ,		lowerCamelCase    ,		lowerCamelCase    ,		lowerCamelCase						):
        super().__init__()
        __a       =    nn.Linear(lowerCamelCase    ,		lowerCamelCase    ,		bias=lowerCamelCase						)
        __a       =    nn.Linear(lowerCamelCase    ,		lowerCamelCase    ,		bias=lowerCamelCase						)
        __a       =    nn.Linear(lowerCamelCase    ,		lowerCamelCase    ,		bias=lowerCamelCase						)
        __a       =    nn.Dropout(lowerCamelCase						)
        __a       =    NewGELUActivation()






 def 						a__   ( self    ,		lowerCamelCase						):
        __a       =    self.act(self.wi_a(lowerCamelCase						)						)
        __a       =    self.wi_a(lowerCamelCase						)
        __a       =    hidden_gelu * hidden_linear
        __a       =    self.dropout(lowerCamelCase						)

        __a       =    self.wo(lowerCamelCase						)
        return hidden_states






class  snake_case__      (       nn.Module       ):


 def __init__( self    ,		lowerCamelCase    ,		lowerCamelCase=1E-6						):
        super().__init__()
        __a       =    nn.Parameter(torch.ones(lowerCamelCase						)						)
        __a       =    eps






 def 						a__   ( self    ,		lowerCamelCase						):
        # T5 uses a layer_norm which only scales and doesn't shift, which is also known as Root Mean
        # Square Layer Normalization https://arxiv.org/abs/1910.07467 thus variance is calculated
        # w/o mean and there is no bias. Additionally we want to make sure that the accumulation for
        # half-precision inputs is done in fp32

        __a       =    hidden_states.to(torch.floataa						).pow(2						).mean(-1    ,		keepdim=lowerCamelCase						)
        __a       =    hidden_states * torch.rsqrt(variance + self.variance_epsilon						)

        # convert into half-precision if necessary
        if self.weight.dtype in [torch.floataa, torch.bfloataa]:
               __a       =    hidden_states.to(self.weight.dtype						)

        return self.weight * hidden_states






class  snake_case__      (       nn.Module       ):


 def 						a__   ( self    ,		lowerCamelCase						):
        return 0.5 * input * (1.0 + torch.tanh(math.sqrt(2.0 / math.pi						) * (input + 0.04_4715 * torch.pow(lowerCamelCase    ,		3.0						))						))






class  snake_case__      (       nn.Module       ):


 def __init__( self    ,		lowerCamelCase    ,		lowerCamelCase						):
        super().__init__()
        __a       =    nn.Linear(lowerCamelCase    ,		out_features * 2    ,		bias=lowerCamelCase						)






 def 						a__   ( self    ,		lowerCamelCase    ,		lowerCamelCase						):
        __a       =    self.scale_bias(lowerCamelCase						)
        __a ,   __a       =    torch.chunk(lowerCamelCase    ,		2    ,		-1						)
        __a       =    x * (1 + scale) + shift
        return x

"""simple docstring"""



from __future__ import annotations

import math



def 	_lowerCamelCase(	a   ,    a				):
       __a       =    u
       for i in range(1   ,    a				):
              __a       =    temp * (u - i)
       return temp



def 	_lowerCamelCase(	):
       __a       =    int(input("enter the numbers of values: "				)				)
       __a       =    []
       for _ in range(a				):
              y.append([]				)
       for i in range(a				):
              for j in range(a				):
                     y[i].append(a				)
                     __a       =    0

       print("enter the values of parameters in a list: "				)
       __a       =    list(map(a   ,    input().split()				)				)

       print("enter the values of corresponding parameters: "				)
       for i in range(a				):
              __a       =    float(input()				)

       __a       =    int(input("enter the value to interpolate: "				)				)
       __a       =    (value - x[0]) / (x[1] - x[0])

       # for calculating forward difference table

       for i in range(1   ,    a				):
              for j in range(n - i				):
                     __a       =    y[j + 1][i - 1] - y[j][i - 1]

       __a       =    y[0][0]
       for i in range(1   ,    a				):
              summ += (ucal(a   ,    a				) * y[0][i]) / math.factorial(a				)

       print(F"the value at {value} is {summ}"				)


if __name__ == "__main__":
   main()
